volume 32, issue 1, P107-115 2004
DOI: 10.1007/s00454-003-0854-z
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Abstract: We derive improved bounds on the complexity, i.e., the total number of faces of all dimensions, of many cells in arrangements of hyperplanes in higher dimensions, and use these bounds to obtain a very simple proof of an earlier bound, due to Aronov, Matoušek, and Sharir, on the sum of squares of cell complexities in such an arrangement.

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